Geodesic
Explicit-implicit schemes for convection-diffusion-reaction problems
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 15 (2012) no. 4, pp. 359-369.

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The basic models of problems in continuum mechanics are boundary value problems for the time-dependent convection-diffusion-reaction equations. For their study, various numerical methods are involved. After applying the finite difference, finite element or finite volume approximation in space, we arrive at the Cauchy problem for systems of ordinary differential equations whose main features are associated with the asymmetry of the operator and its indefinite. The explicit-implicit approximation time is conventionally used in constructing splitting schemes in terms of physical processes, when separated by convection and diffusion transfers, the reaction process. In this paper, unconditionally stable schemes for unsteady convection-diffusion-reaction equations are used, when explicit-implicit approximations are applied in splitting the operator reaction. An example of a model 2D problem in the rectangle is presented. 
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P. N. Vabishchevich; M. V. Vasil'eva. Explicit-implicit schemes for convection-diffusion-reaction problems. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 15 (2012) no. 4, pp. 359-369. http://geodesic.mathdoc.fr/item/SJVM_2012_15_4_a1/

[1] Hirsch Charles, Numerical Computation of Internal and External Flows: Fundamentals of Computational Fluid Dynamics, Elsevier, Butterworth–Heinemann, 2007

[2] Wesseling P., Research in Numerical Fluid Mechanics, Vieweg, Braunschweig, 1987 | MR | Zbl

[3] Tannehill John C., Anderson Dale A., Pletcher Richard H., Computational Fluid Mechanics and Heat Transfer, Taylor Francis, 1997

[4] Morton K. W., Kellogg R. B., Numerical Solution of Convection-Diffusion Problems, Chapman Hall, London, 1996 | MR | Zbl

[5] Samarskii A. A., Vabischevich P. N., Chislennye metody resheniya zadach konvektsii-diffuzii, URSS, M., 1999

[6] Hundsdorfer W. H., Verwer J. G., Numerical Solution of Time-Dependent Advection-Diffusion-Reaction Equations, Springer Verlag, 2003 | MR | Zbl

[7] Samarskii A. A., Teoriya raznostnykh skhem, Nauka, M., 1989 | MR

[8] Samarskii A. A., Gulin A. V., Ustoichivost raznostnykh skhem, Nauka, M., 1973 | Zbl

[9] Samarskii A. A., Matus P. P., Vabishchevich P. N., Difference Schemes with Operator Factors, Kluwer Academic Publ., 2002 | MR | Zbl

[10] Laevskii Yu. M., Gololobov S. V., “Yavno-neyavnye metody dekompozitsii oblasti resheniya parabolicheskikh uravnenii”, Sib. mat. zhurnal, 36:3 (1995), 590–601 | MR | Zbl

[11] Ascher U. M., Ruuth S. J., Wetton B. T. R., “Implicit-explicit methods for time-dependent partial differential equations”, SIAM J. on Numer. Anal., 32:3 (1995), 797–823 | DOI | MR | Zbl

[12] Ruuth S. J., “Implicit-explicit methods for reaction-diffusion problems in pattern formation”, J. of Mathematical Biology, 34:2 (1995), 148–176 | DOI | MR | Zbl

[13] Vabishchevich P., Vasil'eva M., Iterative Methods for Solving the Pressure Problem at Multiphase Filtration, Ithaca, 2011; Preprint Cornell University Library, arXiv: 1107.5479

[14] Samarskii A. A., Nikolaev E. S., Metody resheniya setochnykh uravnenii, Nauka, M., 1978 | MR